Generally speaking, USCIS looks at the last five years preceding the application, but they CAN go back as long as they wish for adjudicating good moral character. My guess is, you should be fine.
If he was out of USA for more than one year at any one time, the reentry permit will allow him to file after 4 years and 1 day from re-establishing domicile in USA.
From what you have described it does not appear you have a criminal conviction. Nevertheless, in my view, you should get yourself a local lawyer to assist you with the naturalization process.
Temporary absence of three months while your citizenship application is pending should not pose a problem as long as you remain a permanent resident of USA.
I am assuming she has been a green card holder for 5 years the form is N-400.
Thanks for your kind comments about our web site. You can apply, but USCIS can certainly make an issue about the misdemeanor. You may want to retain a local lawyer.
I see no problem with the visits - they were all less than 6 months. I think it should be ok. It is difficult to estimate how long it will take.
As far as I know they rely upon your passport and their own entry-exit records through Form I-94 system. This situation is common and can be corrected by supplying affidavits from applicants along with any other evidence you may have.
Quote: A member of our family was issued a Green Card in November 1980. The green card did not have any renewal date (see enclosed). I assume Green Cards at that time did not have a renewal date. Does this need to be renewed?
Ans: Replace the green card. See: